The harmonic balance method with arc-length continuation in blade-tip/casing contact problems

On Harmonic Balance Method-based Lagrangian contact formulations for vibro-impact problems

“…The latter are being adressed in this paper. This subject of research is highly active, as shown by the wide variety of predictive numerical strategies developed to accurately describe contact interactions [1,4,6,16,18,21,23,26,27,33,34,35]. Time marching strategies [4,16,27,33,34] are usually privileged since they only require few approximations on the solutions.…”

“…Another typical application of the HBM may be found in the field of turbomachinery where the whole system is under periodic aerodynamic and mechanical forcing due to the rotation of the shafts. Therefore, it is widely used on industrial applications in the field of nonlinear dynamics applied to bladed disks in terms of friction damping [petrov˙high-accuracy˙2010, 29,47], geometric nonlinearities [14,25] and rubbing interactions [6,38]. The methodologies allowing to account for nonlinearities in numerical simulations are usually classified according to the type of nonlinearity at stake.…”

“…Contact nonlinearities associated with the HBM come with a difficulty inherent to the frequency formulations: Coulomb's law and Hertz-Signorini-Moreau conditions must be applied in the time domain, thus standard strategies to evaluate the nonlinear contact forces are a part of an Alternating Frequency-Time (AFT) procedure [2,3,6,7,15,20,29,36,39,42,43], the AFT procedure was assessed in [43] on both smooth and nonsmooth applications. The nonsmooth behaviour of contact interactions has widely been studied by means of the HBM.…”

“…When it comes to unilateral contact, several contact treatments exist in order to compute nonlinear forces. A large majority of the methodologies rely on a penalty-based contact treatment [2,6,7,9,11,18,20,23,31,36,43,44]. For some applications, the latter being too challenging from a numerical standpoint, an additional regularization is added [6,18,43,44] to smoothen the nonsmoothness of contact forces.…”

“…A large majority of the methodologies rely on a penalty-based contact treatment [2,6,7,9,11,18,20,23,31,36,43,44]. For some applications, the latter being too challenging from a numerical standpoint, an additional regularization is added [6,18,43,44] to smoothen the nonsmoothness of contact forces. To the contrary, the Dynamical Lagrangian Frequency-Time associated with HBM (DLFT-HBM) directly simulates the unilateral contact law [29] without requiring a penalty-based contact treatement.…”